Thermodynamics from the differential geometry standpoint |
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Authors: | V P Pavlov V M Sergeev |
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Institution: | (1) Steklov Mathematical Institute, RAS, Moscow, Russia;(2) Center for Studying Global Problems, Moscow State Institute of International Relations, Moscow, Russia |
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Abstract: | We study the differential-geometric structure of the space of thermodynamic states in equilibrium thermodynamics. We demonstrate
that this space is a foliation of codimension two and find variables in which the foliation fibers are flat. We show that
we can introduce a symplectic structure on this space: the external derivative of the 1-form of the heat source, which has the form of the skew-symmetric product dT 蝃 dS in the found variables. The entropy S then
plays the role of the Lagrange function (or Hamiltonian) in mechanics, completely determining the thermodynamic system.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 141–148, October, 2008. |
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Keywords: | symplectic structure space of states dynamical principle |
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